Yes, you can sell off part of your business and keep control.
In general there are two types of situations when selling off part of your business is viable
Naturally any new investors will consider whether the corporate governance arrangements can sufficiently protect their minority investment, which is usually done through a shareholders agreement. Shareholders agreements may cover issues such as directors, sale of shares, approval of major transactions, dividends, reporting and liquidity
I am particularly a fan of the progressive sell down, as part of an exit planning exercise